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Equation of time adjustment on the sundial

You may have noticed that the sun is higher in the sky in summer than in winter. As a result, each day, the tip of the shadow will follow a slightly different path across the hour lines. These paths are called diurnal arcs. They range between two extremes: the summer solstice, when the sun is highest in the sky, and the winter solstice when it is lowest. The solstices generally fall on June 20/21 and December 21/22.

In the diagrams below, Calcad has drawn, in purple, the diurnal arcs for the winter and summer solstices and the changeover dates for the astrological signs. The central arc, the equinoctial, is a straight line corresponding to the equinoxes (March 20/21 and September 22/23).

If you choose to integrate the equation of time adjustment directly on the sundial by drawing the hour curves, Calcad calculates the exact position of the shadow's tip for each diurnal arc, including the adjustment. The resulting curves snake between the solstices, in the shape of an inverted "S" for the months from July to December, shown in red in all three diagrams, and an "S" for the months from January to June, shown in blue in the third diagram. Together, the complete hour curves form a figure-8 shape called an analemma.

Note: If you choose to draw the diurnal arcs for the first of each month, Calcad uses the same color as the corresponding "S" curves.

Adjustment of the equation of time from July to December
In the pictures, the shadow is on the diurnal arc for October 23 and it is exactly 14:00

Except for the arc of the equinoxes, which is a straight line, all the diurnal arcs and hour curves are complex shapes (you can't just draw a straight line between their end points). To make it easy to reproduce them on the sundial, choose Squares in the Other menu. Calcad will then superimpose a grid on the diagram, as shown below. You can adjust the size of the squares in the input box.

Superposition of the curves for the whole year.

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